Gustavo Patraín has been a loyal supporter of President Chávez for the past 14 years. "He's the man, the leader, the ultimate," he says, as he looks up from underneath the bonnet of the burgundy 1976 Dodge Coronet he is attempting to repair.

And, according to the government, the mechanic is currently also a close neighbour of the ailing president. The windowless two-room brick home he shares with his wife, and three of his five children, is overlooked by the Carlos Arvelo military hospital.

It is here, on the eighth floor, that Chávez is apparently being treated. A huge, garish poster of the former paratrooper, in robust health, has been fixed to one side of the building. Pictures of the leader hugging an elderly woman, with the words "Chávez: live, and smile" adorn the broken pavements outside.

But Gustavo is not convinced. "Is he really there? We need to know," he says. "They should let one of us, the people, go and see him. So far it has only been the government."

No images at all have been released of Chávez in Venezuela following his pre-dawn return from his latest treatment in Cuba. Instead the government has issued vague, but increasingly pessimistic, reports on his condition. On Thursday the vice-president, Nicolás Maduro, seemed to hint that the end was near. The president, he said, is "battling for his health and his life … and we are accompanying him." He went on to say that Chávez "gave his life to those that don't have anything". And on Friday, at a special mass for the president held at the hospital, he said that the president was undergoing chemotherapy, quoting Chávez as saying he was entering "a new phase" of "more intense and tough" treatments and wanted to be in Caracas for them.

Outside the hospital, a handful of soldiers from the presidential guard, easily distinguished by their bright red berets, give the impression that the man who has led this oil-rich nation since 1999 is inside. Occasionally they stop a car or a motorbike at the entrance and make a cursory inspection. State media have reported that it is on Chávez's personal instructions that the hospital, which prior to his rule was only for the military's use, should continue to operate normally as a public hospital, despite his presence.

Belinda, 39, has spent the last month living inside the building. She was there before the president's arrival was announced, caring for her mother, who suffered a stroke in January. She says that the day she heard the president had returned to Venezuela, three upper floors of the hospital were sealed off and the entire building was cleaned. "But last weekend everything went back to normal," she adds. "I think he is there. But I am not sure he is alive."

Caracas is awash with such rumours. On Friday, officials, including the vice-president, responded. They lashed out at what they described as the "fascist" international media for spreading lies in an attempt to destabilise the country. They singled out the Spanish newspaper ABC, which has published unsourced claims that Chávez has decided to spend his dying days at the presidential retreat of La Orchilla in the Caribbean, surrounded by his family. Jorge Arreaza, Venezuela's science minister, who is married to the president's eldest daughter, dismissed the report as "bizarre and unfounded".

But the speculation is fuelled by the government's own secrecy about the nature and severity of the president's cancer. In June 2011 he revealed that a baseball-size tumour had been discovered, and removed, from his pelvic area. On two occasions Chávez has declared he was free of cancer, most recently while campaigning for re-election in October, an election he won by a comfortable margin. But last December the president revealed that the cancer had returned, and that he required a fourth operation.

Before he left for Cuba that final time, Chávez appeared on national television. Seemingly aware of the gravity of his illness, he said that, if the treatment he was about to undergo left him incapacitated "in any way", new presidential elections should be held and the people should vote for Vice-President Maduro. Clutching a copy of the constitution, he emphasised that this was his "absolute, irrevocable" belief. He then kissed his crucifix.

Maduro, a bus driver turned union leader, who has become the president's closest aide and friend, sat alongside him. He looked uncomfortable. Diosdado Cabello, the former soldier who now serves as head of the National Assembly and is seen as a possible rival to Maduro, remained impassive.

But despite Chávez's clear, and prescient, command, his juniors seem to have ignored it, or at least decided the moment has not yet arrived when they should follow his instructions.

On 10 January, when Chávez should have been inaugurated to start his fourth presidential term, the date simply came and went. A celebration party was held in his absence. The loyalist supreme court meanwhile decreed that Chávez was entitled to delay this process just as long as he chooses.

Maduro now appears to be running the country, but he firmly rejects the title "acting president" and insists that Chávez remains well enough to give instructions. Last week it was announced that the president participated – presumably from his hospital bed – in a five-hour series of meetings, covering a range of issues from national security to the economy.

At a late-night press conference afterwards, Maduro conceded that Chávez is unable to speak because of a tracheal tube to assist his breathing, but has been able to contribute to the meetings via what the vice-president described as "a variety of means of writing". Venezuelan diplomats have meanwhile delivered several letters, purportedly from the leftist leader, including one to Cuba's Raúl Castro, congratulating him on his re-election as president.

"The process of beatification has begun," says Carlos Calderón, a Caracas-based lawyer. "Hugo Chávez is becoming a figure of the unconscious, in the background, whose 'wishes' are being fulfilled by his ministers."

Chávez's matchless talent at speaking to the poor in Venezuela – together with the billions of petrodollars which have been spent on social programmes – have earned him a quasi-religious reverence from his followers. But he remains a singularly divisive figure and the country is split almost evenly when it comes to evaluating his charms – he is loved by his supporters just as he is loathed by his opponents.

"He's the sort of president who only comes around perhaps every two centuries," says Francisco Morón, speaking from his new three-bedroom home, which he was given by the government last year after 25 years of homelessness.

The government has encouraged Venezuelans to attend church services and pray for their sick leader.

On Friday, a new chapel was opened in the grounds of the Carlos Arvelo hospital and a mass was held, attended by senior members of the government.

Meanwhile, Venezuela's opposition is slowly preparing for the possibility of new elections. The diverse, sometimes fractious, parties have yet to choose a single candidate, but are widely assumed, once again, to select the youthful governor of Miranda state, Enrique Capriles. Capriles lost against Chávez last October, but secured nearly 45% of the national vote, by far the best electoral showing for the opposition in years.

Despite widely perceived failings of the Chávez government – including soaring crime, the highest inflation in Latin America, five devaluations of the currency and chronic infrastructure decay – the opposition has so far failed to attract sufficient numbers of disgruntled Chavista voters to its cause.

But its leaders do see a possible opportunity in the current crisis, particularly if those around the ailing president are shown to have misled his supporters. "I don't believe we should spend every day asking where Chávez is," says opposition legislator Ismael García. "He is clearly in a bad way, and one day they need to end this lie."

Across Caracas, huge billboards, put up before October's elections, proclaim "we all are Chávez". The message is that Chávez's political movement, Chavismo, is more than one man, and presumably can survive him

But Gustavo's admiration for Chávez is almost matched by his distrust of the men whose task may be to keep the president's legacy alive.